A Characterisation of Optimal Channel Assignments for Cellular and Square Grid Wireless Networks

In this paper we first present a uniformity property that characterises optimal channel assignments for networks arranged as cellular or square grids. Then, we present optimal channel assignments for cellular and square grids; these assignments exhibit a high value for δ₁ – the separation between channels assigned to adjacent stations. We prove an upper bound on δ₁ for such optimal channel assignments. This upper bound is greater than the value of δ₁ exhibited by our assignments. Based on empirical evidence, we conjecture that the value our assignments exhibit is a tight upper bound on δ₁.